(0,2)型张量场诱导的线性变换的显表达式提取方法

College Mathematics（2011）

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Abstract

对于黎曼流形(M,g)上(0,2)型光滑张量场R诱导出的线性变换R*:X(M)→X(M),其隐表达式为g(R*(X),Y)=S(X,Y),X,Y∈X(M),研究了从局部上提取出R*(X)的显表达式的方法.提出一种所谓g正定提取方法,并将这种方法进一步应用到度量保形变换下的线性变换Φ*(X),L*(X).

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Key words

(r,Ricci transformation R*(X),s)-type smooth tensor,conformal change of metric,trace of linear transformation,distilling method by positively definite metricg

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